Answer
$\text{LCD: }
75ab^2c^3
\\\\\text{Equivalent of 1st Expression: }
\dfrac{55a^2c^2}{75ab^2c^3}
\\\\\text{Equivalent of 2nd Expression: }
\dfrac{42b^3}{75ab^2c^3}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To find the $LCD$ of the given expressions, $
\dfrac{11a}{15b^2c}
$ and $
\dfrac{14b}{25ac^3}
,$ express the denominators in factored form. Then take the highest exponent of each factor. Finally use the $LCD$ to find the required equivalent expression for the given.
$\bf{\text{Solution Details:}}$
In factored form, the given expressions are equivalent to
\begin{array}{l}\require{cancel}
\dfrac{11a}{3(5)(b^2)(c)}
\text{ and }
\dfrac{14b}{(5^2)(a)(c^3)}
.\end{array}
Taking the highest exponent of each factor, then the $LCD$ is
\begin{array}{l}\require{cancel}
3(5^2)(a)(b^2)(c^3)
\\\\=
3(25)(a)(b^2)(c^3)
\\\\=
75ab^2c^3
.\end{array}
Multiplying the given expression by an expression equal to $1$ such that the denominator becomes the $LCD,$ then the given expressions are equivalent to
\begin{array}{l}\require{cancel}
\dfrac{11a}{15b^2c}
\cdot\dfrac{5ac^2}{5ac^2}=
\dfrac{55a^2c^2}{75ab^2c^3}
\\\\\text{ and }\\\\
\dfrac{14b}{25ac^3}
\cdot\dfrac{3b^2}{3b^2}=
\dfrac{42b^3}{75ab^2c^3}
.\end{array}
Hence, the needed pieces of information are as follows:
\begin{array}{l}\require{cancel}
\text{LCD: }
75ab^2c^3
\\\\\text{Equivalent of 1st Expression: }
\dfrac{55a^2c^2}{75ab^2c^3}
\\\\\text{Equivalent of 2nd Expression: }
\dfrac{42b^3}{75ab^2c^3}
.\end{array}
